WASHINGTON STATE MATHEMATICS COUNCIL 2000 MIDDLE SCHOOL MATH OLYMPIAD   Session II: EIGHTH GRADE NUMBER SENSE Make sure you include proper units in your answer! 8

1.   Lara, Rosa, and Pam work out at the Fitness Center after school as often as their schedules permit them to.   Lara works out every 4 days, Rosa works out every 6 days, and Pam, who plays in the band after school, is only able to work out every 14 days.   During the next 12 weeks:

(a)   how many days will only Rosa and Pam work out on the same days?

(b)   how many days will only Lara and Rosa work out on the same days?

2.   Ann is the weakest foul shooter on the girls' basketball team.   Out of her first 30 foul shots, she made only 50%.   Her coach had her go through several practice sessions.   She raised her season's percent to 60% after 20 more foul shots in the next three games.   How many of these 20 shots did she make?

3.   A person born in the latter part of the nineteenth century was y years old in the year y-squared.   In what year was this person born?

4.   In what bases (less than or equal to 10) is the number 2,101 a perfect square?

5.   Given the following table, determine the next two rows.

1       1      1

1       2      3       2       1

1       3      6       7       6       3       1

1       4     10     16     19     16     10       4       1